Phononic Band Gaps Research Articles

Enhanced ultrasonic wave generation using energy-localized behaviors of phononic crystals

This paper aims to bridge the energy-localized behaviors of a phononic crystal (PnC) and an ultrasonic-wave-generation (UWG) system. A defective PnC manifests an intriguing phenomenon in which input ultrasonic-wave energy is confined near the defect in several defect-band frequencies that appear in the phononic band-gap range. Using the inverse of this energy localization, remarkably amplified ultrasonic waves can be generated compared to a UWG system without the PnC. This work proposes an analytical model that predicts the UWG system's sensitivities and electrical admittance. The mechanical equation of motions and the electrical circuit equation of the piezoelectric-patch-bonded defect are derived using the Rayleigh-Love rod theory and the extended Hamilton's principle. Through the use of Green's functions, these electroelastically coupled equations are solved. With two assumptions, specifically, (i) continuity conditions throughout the PnC and (ii) no incident waves toward the UWG system, the S-parameter-method-based analytical approach presents the system performances explicitly. Furthermore, the modified analytical model for application to engineering situations with finite boundary conditions is also proposed. The predicted results of the proposed analytical model match well with those of the finite element model and show that the UWG performances are amplified to several times their prior value. The main contributions of this work are as follows: (i) this is the first attempt to utilize a defective PnC as UWG systems, (ii) the analytical model is newly proposed and dramatically shortens the computational time compared to the finite-element-method, and (iii) the proposed defective-PnC-incorporated UWG system and its analytical model are effective, regardless of the boundary conditions.

Photo-Elastic Enhanced Optomechanic One Dimensional Phoxonic Fishbone Nanobeam

We investigated the strength of acousto-optical (AO) interaction in one-dimensional fishbone silicon nanobeam computationally. The structure can generate phononic and photonic band gaps simultaneously. We use defect cavity optical mode and slow light mode to interact with acoustic defect modes. The AO coupling rates are obtained by adding the optical frequency shifts, which result from photo-elastic effect and moving-boundary effect disturbances. The AO coupling rates are strongly dependent on the overlap of acoustic and optical mode distribution. The strength of AO interaction can be enhanced by choosing certain acoustic defect modes that are formed by the stretching of wings and that overlap significantly with optical fields.

Theoretical Investigation of Magneto-Electro-Elastic Piezoelectric Phononic Crystal

We design a magneto-electro-elastic piezoelectric phononic crystal (MPPC) using a one-dimensional piezoelectric superlattice (with a 3m point group) and split-ring resonators. The effect of the split-ring resonators is to enhance the piezoelectric effect of the piezoelectric superlattices. This effect will create elastic anomalies and generate the phononic band gaps. These are first proposed theoretically. We calculate the transmission function of the MPPC through Transfer Matrix Method of the phononic crystal. By using the transmission function, we theoretically study the propagation properties of the acoustic waves in the MPPC. The mechanism for multifield coupling is analyzed. A type of phononic band gap is created, called the multifield coupling phononic band gap. We analyze the possibility of crystals as left-handed metamaterials. We also discuss some potential applications.

Effect of High Order Phonon Scattering on the Thermal Conductivity and Its Response to Strain of a Penta-NiN2 Sheet.

Motivated by the recent synthesis of penta-NiN2, a new two-dimensional (2D) planar material entirely composed of pentagons [ ACS Nano 2021, 15, 13539], we study its thermal transport properties based on first-principles calculations and solving the Boltzmann transport equation within the self-consistent phonon theory and four-phonon scattering formalism. We find that the intrinsic lattice thermal conductivity of penta-NiN2 is 11.67 W/mK at room temperature, which is reduced by 89.32% as compared to the value obtained by only considering three-phonon scattering processes. More interestingly, different from the general response of thermal conductivity to external strain in most 2D materials, an oscillatory decrease of the thermal conductivity with increasing biaxial tensile strain is observed, which can be attributed to the renormalization of vibrational frequencies and the nonmonotonic variation of phonon scattering rates. This work provides an accurate intrinsic thermal conductivity of penta-NiN2 and elucidates the effects of the strain-tuned vibrational modes and phonon band gap on the four-phonon scattering processes, shedding light on a better understanding of the physical mechanisms of thermal transport properties in 2D pentagon-based materials.

Planes approximation method for investigating the physical origins of deep, wide phononic bandgaps

The objective of this paper is to formulate a simple analytical model that describes Bragg and Mie scattering leading to the creation of bandgaps in phononic crystals (PnCs). The model is a homogenized, mean-field 1D model, dubbed the Planes Approximation Method (PAM). Bragg and Mie scattering are decoupled into independent 1D models and then recombined graphically to understand better and visualize bandgap creation. Due to the model's simplicity, it allows for rapid solutions compared to other computational methods. This paper argues that acoustic impedance mismatches yield bandgaps based on the formulation. PAM is demonstrated using a square lattice of microscale circular inclusions of tungsten with a lattice constant of 45 μm in a SiO2 matrix and then compared to results from finite difference time domain and plane wave expansion simulations.

Optimization and inference of bin widths for histogramming inelastic neutron scattering spectra.

A data-driven bin-width optimization for the histograms of measured data sets based on inhomogeneous Poisson processes was developed in a neurophysiology study [Shimazaki & Shinomoto (2007). Neural Comput. 19, 1503-1527], and a subsequent study [Muto, Sakamoto, Matsuura, Arima & Okada (2019). J. Phys. Soc. Jpn, 88, 044002] proposed its application to inelastic neutron scattering (INS) data. In the present study, the results of the method on experimental INS time-of-flight data collected under different measurement conditions from a copper single crystal are validated. The extrapolation of the statistics on a given data set to other data sets with different total counts precisely infers the optimal bin widths on the latter. The histograms with the optimized bin widths statistically verify two fine-spectral-feature examples in the energy and momentum transfer cross sections: (i) the existence of phonon band gaps; and (ii) the number of plural phonon branches located close to each other. This indicates that the applied method helps in the efficient and rigorous observation of spectral structures important in physics and materials science like novel forms of magnetic excitation and phonon states correlated to thermal conductivities.

Elastic anisotropy and wave propagation properties of multifunctional hollow sphere foams

Obtaining multifunctionality from microstructures instead of constituents provides a new direction for developing multifunctional materials. Periodic hollow sphere foams (HSFs) offer one lightweight structural motif with open and closed cells, high energy absorption, low thermal conductivity, snap-through instability, and triple-negative material indices. Here, we investigate the direction-dependent mechanical property, instability, and elastic wave isolation behavior of HSFs. Explicit formulas, stereographic projections, and general scaling relationships are developed to quantify and visualize the anisotropic mechanical properties of HSFs. By investigating the directional wave propagation in HSFs, extremely wide phononic band gaps are identified in the HSFs. The derived formulas and the simulation-informed parametric maps allow the design of HSFs with desired static and dynamic anisotropic property profiles, including tailorable direction-dependent stiffness/shear modulus, negative Poisson’s ratio, and wave isolation properties. Building upon these results, multifunctional design concepts of HSFs are further set forth. This study not only reveals tailorable mechanical anisotropy and band gap in HSFs, but also develops a general approach to investigate the direction-dependent properties of periodic materials, enabling multifunctional applications where lightweight, direction-dependent property, wave attenuation, and programmability are required simultaneously.

Electrically tunable topological interface states in one-dimensional nanomechanical lattices

In optics, combining one-dimensional (1D) topological systems with lasers and nonlinear optics has promoted their rapid development. A 1D acoustic topological system can only achieve single-frequency acoustic waves localization, limiting its practicality. The implementation of tunable and integrated 1D topological systems will improve this situation. Here, we propose an electrically tunable and integrable 1D topological nanoelectromechanical phononic crystal. Different strong and weak couplings are formed by changing the overlapping degree of adjacent suspended circular membranes, accompanied by different topological properties for the phononic bandgaps. Topologically protected interface states exist at their interface, and these states are stable even after introducing various degrees of distortion. Narrow band-pass filters based on these interface states can be implemented, with adjusted operating frequency by different grid voltage. Our proposed electrically tunable and integrable structure holds potential for smart filtering and may facilitate the development of integrated electromechanical circuits.

Design and optimization of three-dimensional composite multilayer cylindrical pentamode metamaterials for controlling low frequency acoustic waves

For three-dimensional pentamode metamaterials, it is of great significance to realize underwater low frequency acoustic wave control. Therefore, in order to compare with traditional double-cone pentamode metamaterials, two multilayer composite cylindrical three-dimensional pentamode metamaterials with low frequency and broad band gaps are proposed in this paper. By using pentamode metamaterials with lattice constants on the order of centimeters, the phononic band gaps below 60 Hz and the single-mode area below 30 Hz can be obtained. In addition, compared with asymmetrical double-cone locally resonant pentamode metamaterials, the lower edge frequency, relative bandwidth and figure of merit of the first phononic band gap can be reduced by up to 61.4%, 10.3% and 40.6%, respectively. It will provide reference and guidance for the engineering application of pentamode metamaterials in controlling the ultra-low frequency broadband acoustic waves, vibration and noise reduction.

Wave propagation in a continuum phononic material with geomaterial-inspired nonlinearity

This presentation discusses the nonlinear wave propagation in a continuum phononic material with nonlinear mechanisms inspired by geomaterials. Geomaterials can exhibit nonlinear wave responses due to mechanisms such as material nonlinearity or lack of bonding between phases of material. We study the interaction of nonlinear and phononic behavior by introducing two geomaterial-inspired nonlinear mechanisms into a phononic material. The influence of material nonlinearity and nonlinearity due to delaminations between material phases are studied in a bilayer finite element model composed of alternating layers of stiff linear elastic material and soft hyperelastic material. To model delaminations, a binary contact condition is applied at the interface between layers. Measurements of the quasi-static nonlinear mechanical response of delaminations of different lengths are used as inputs into the finite element method simulations. The influence of the delamination nonlinearity plus material nonlinearity on the phononic material is studied in a full-scale time-domainfinite element model. This model is used to further probe the interaction between phononic band gaps and nonlinear wave response, as well as the dependence of delamination size and location on the nonlinear wave response.

Dispersion and band gaps of elastic guided waves in the multi-scale periodic composite plates

This paper presents dispersive behaviors and band gap characteristics of the multi-scale periodic composite plate reinforced with grapheme platelets (GPLs) and fibers. The plate consists of a laminated composite structure and an isotropic part. The material properties are measured by the layer-wise distribution of graphene platelets (GPLs) in nanocomposite matrix and fiber content in the laminated composite. Based on the first order shear deformation plate theory, Bloch theorem and the higher-order spectral elements, a semi-analytical approach is proposed for wave analysis of the periodic laminated composites. Considering the periodic boundary and analytic integration through the thickness, elastodynamic wave equation is established on the middle surface of the periodic unit cell, and then transformed into a one-dimensional problem by the Fourier transformation along the wave propagation direction, which improves the calculation efficiency. A second-order polynomial eigenvalue problem with regard to wave dispersion is obtained. Besides, the accuracy of the proposed approach is analyzed and the layer number of the nanocomposite laminate is determined. Various significant parameters including weight content of GPLs, fiber volume fraction and lattice size of the plate are taken into account to investigate guided wave propagation in the multi-phase periodic composite plates. The results indicate that full band gaps can be realized in the periodic multi-scale composite phononic crystal plates and partial band gaps appear in both in-plane and out-of-plane wave modes. The addition of reinforcements can efficiently regulate the center frequency and width of full and partial band gaps by changing GPLs content and fiber volume. Moreover, the variation of lattice parameter of the periodic composite plate has significant impact on the first full band gap. This work can provide guidelines to the developments of novel composite structures, acoustic devices and the applications in structural health monitoring.

Tunable phononic bandgap materials designed via topology optimization

Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

Investigating Electronic, Optical, and Phononic Properties of Bulk γ-M2ON2 and β-M7O8N4 (M = Hf and Zr) Insulators Using Density Functional Theory.

Hafnium and zirconium oxynitrides have similar properties, yet a consolidated investigation of their intrinsic properties has not been carried out. In this paper, we perform first-principles density functional theory calculations of γ- and β-phase hafnium and zirconium oxynitrides, which show that the γ-M2ON2 (M = Hf and Zr) is an indirect band-gap (Eg) insulator, while the β-M7O8N4 has a “pseudo-direct” type of Eg. β-phase has higher Eg than γ-phase, with concomitant disappearance of the conduction band tail. Optical properties in γ-M2ON2 show that the anisotropy is negligible, and the optical constant values are in the range of other superhard materials. Phonon calculations present peculiar characteristics such as a small phonon band gap in γ-Hf2ON2 and imaginary phonon frequencies in β-phases relating to lattice instability. The phononic properties are unfavorable for their potential use as an absorber material of the hot carrier solar cell—an emerging photovoltaic concept.

Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation

AbstractSoft cellular mechanical metamaterials (CMMs) have gained increasing attention due to their unique mechanical properties, especially when under large deformation. However, the strong nonlinearities and complex instabilities brought by the large deformation field is a critical challenge for the rational design of soft CMMs. In this work, we propose a mapped shape optimization method as a computational framework for inverse designs of soft CMMs. The core of this method is to introduce a fixed referential configuration. The geometric changes of the cellular structures are reflected by altering a differentiable shape map; and the deformation of the corresponding structures are determined by mapping the finite element computations to the referential configuration. Such formulation avoids the need to alter the background mesh and more importantly, provides an efficient way to compute the gradient of the objective functions with respect to the design variables via the adjoint method. The proposed method is of general purpose, and three distinct yet representative numerical examples are used to demonstrate the effectiveness of the method: optimizing unique overall mechanical properties, precise control of the onset of instability, and optimizing phononic band gaps. These examples cover a broad range of important engineering applications of soft CMMs.

Triple tunability of phononic bandgaps for three-dimensional printed hollow sphere lattice metamaterials

Sound and vibration pollution is ubiquitous in urban areas. How to alleviate the pollution has been concerned because of their broad frequency range. Currently, phononic crystals (PCs) are potential candidates for solutions. However, specific geometry, mass, and stiffness of PCs produce only fixed narrow bandgaps. Many PCs can only be tuned from one bandgap to the other. Here, in order to realize triply or multiply tunable phononic bandgaps, we introduce the three-dimensional (3D) printed hollow sphere lattice metamaterials. Utilizing the reversible temperature-dependent stiffness of the glassy polymer and discontinuity of stable thermal field in the lattice structure, we soften triply the binders between hollow spheres, keep hollow spheres hard, and attain triple modulation of the phononic bandgaps, which was validated by conducting low-amplitude transmission testing and numerical simulations. The results show that phononic bandgaps can be magnified by 37.5%. The findings reported here provide a path for designing phononic lattices with controllable and broad band gaps, offering extensive potential applications in acoustic and vibration suppression, wave guiding or filtering, and non-destructive testing.

Non‐Uniform Strain Engineering of 2D Materials

Abstract2D materials are elastic substances that can sustain high strain. While the response of these materials to spatially uniform strain is well studied, the effects of spatially non‐uniform strain are understood much less. In this review, we examine the response of two different 2D materials, transition metal dichalcogenides and graphene, under non‐uniform strain. First, we analyze pseudo‐magnetic fields formed in graphene subjected to highly localized non‐uniform strain. Second, we discuss the effect of non‐uniform strain on excitons in non‐uniformly strained TMDC. We show that while transport or “funneling” of excitons is relatively inefficient, a different process, a strain‐related conversion of excitons to trions is dominant. Finally, we discuss the effects of uniform and non‐uniform strain in a graphene‐based phononic crystal. We find that uniform strain can be used to broadly tune the frequency of the phononic bandgap by more than 350 % and non‐uniform strain smears that bandgap.

Acousto-optical coupling of the side surface acoustic and optical waves in a two-dimensional phoxonic crystal slab hetero-structure cavity

Phoxonic crystal is a kind of artificial periodic structure which can manipulate light and sound in the same time and space domain. It has good application prospect in optical communication system and opto-mechnical sensor. In this paper, a two-dimensional silicon phoxonic crystal slab structure is proposed, which can exhibit large phononic and photonic bandgaps simultaneously. Then a periodic cylindrical structure is introduced on the side surface of the slab. The effects of the height and radius of the cylinder on the side surface wave modes are analyzed. On this basis, a phoxonic crystal hetero-structure cavity composed of cylinders with different radii and heights is constructed, which can simultaneously confine the acoustic and optical modes because of mode gap effect. Seven phononic cavity modes and two photonic cavity modes are obtained. The two photonic cavity modes are called dielectric mode and air mode respectively. Further, the acousto-optical coupling rates between the seven phononic cavity modes and dielectric mode are calculated. Finally, a gap is etched on each cylinder in hetero-structure cavity, which can increase the surface area of the cavity by 23%. Then two phononic cavity modes and photonic dielectric mode with higher coupling rates are considered. The results show that etching the z-direction gap in the center of the cylinder can effectively increase the acousto-optical coupling rates.

Design of Phononic Bandgap Metamaterials Based on Gaussian Mixture Beta Variational Autoencoder and Iterative Model Updating

AbstractPhononic bandgap metamaterials, which consist of periodic cellular structures, are capable of absorbing energy within a certain frequency range. Designing metamaterials that trap waves across a wide wave frequency range is still a challenging task. In this paper, we present a deep feature learning-based design framework for both unsupervised generative design and supervised learning-based exploitative optimization. The Gaussian mixture beta variational autoencoder (GM-βVAE) is used to extract latent features as design variables. Gaussian process (GP) regression models are trained to predict the relationship between latent features and properties for property-driven optimization. The optimal structural designs are reconstructed by mapping the optimized latent feature values to the original image space. Compared with the regular variational autoencoder (VAE), we demonstrate that GM-βVAE has a better learning capability and is able to generate a more diversified design set in unsupervised generative design. Furthermore, we propose an iterative GM-βVAE model updating-based design framework. In each iteration, the optimal designs found property-driven optimization is used to update the training dataset. The GM-βVAE model is re-trained with the updated dataset for the optimization search in the next iteration. The effectiveness of the iterative design framework is demonstrated by comparing the proposed designs with the designs found by the traditional single-loop design method and the topologically optimized designs reported in literatures. The caveats to designing phonic bandgap metamaterials are summarized.

Phononic real Chern insulator with protected corner modes in graphynes

Higher-order topological insulators have attracted great research interest recently. Different from conventional topological insulators, higher-order topological insulators do not necessarily require spin-orbit coupling, which makes it possible to realize them in spinless systems. Here, we study phonons in 2D graphyne family materials. By using first-principle calculations and topology/symmetry analysis, we find that phonons in both graphdiyne and $\gamma$-graphyne exhibit a second-order topology, which belongs to the specific case known as real Chern insulator. We identify the nontrivial phononic band gaps, which are characterized by nontrivial real Chern numbers enabled by the spacetime inversion symmetry. The protected phonon corner modes are verified by the calculation on a finite-size nanodisk. Our study extends the scope of higher-order topology to phonons in real materials. The spatially localized phonon modes could be useful for novel phononic applications.

Specular Acoustic Vibrational Wave Transmissions with the Presence of Phononic Bandgaps

Specular Acoustic Vibrational Wave Transmissions with the Presence of Phononic Bandgaps